Attack and Defence
To use Poisson Distribution to predict the outcome of a match, you first need to calculate a value for each team’s “Attack” and “Defence Strength”.
These represent how likely a team is to score or concede a goal. As no games have started this season, we have to get relevant data from the nearest possible opportunity – last season.
The number of games in the season (38) should help create a more accurate picture, with freak results averaged out.
The number of Premier League goals scored away in the 2010/11 season was 446, and at home it was 617. The number of goals conceded per season are the same, as the number of goals scored a season equal the number conceded.
To calculate the “Attack Strength”, you first work out the average number of goals scored person season, per game, per team. In mathematical terms, that’s: ([Season Goals Scored] / [Number of Teams]) / [Number of Games].
For the 2010/11 season, that’s 446 / 20 / 18 – the latter number being the number of games played away from home per season per team. The total is 1.174 goals away from home, and 1.624 at home.
You then need to take into account the difference from the average for the teams involved. Since Chelsea are playing away from home, we have to calculate their “Attack Strength” based on away goals.
Chelsea scored 30 goals on-the-road last year, or 1.579 per game. By dividing this figure by the season’s average goals per game, we calculate the team’s “Attack Strength”: 1.345 – or 34.5% higher than average.
While this means Chelsea may score 1.579 against a hypothetical “average” side, it’s important to remember that no team – especially Stoke, with their good home defence, are precisely average.
That’s why, using a similar method to above, we need to work out the Potter’s “Defence Strength”. The season average for goals conceded at home is still 1.174 – although Stoke managed 0.947.
This means their “Defence Strength” is 0.947 divides by 1.174: 0.807 (or 19.3% better than average).
By multiplying Chelsea’s Attack Strength, Stoke’s Defence Strength and the average number of games per season (1.345 * 0.807 * 1.174), we can work out the most likely number of goals Chelsea will score: 1.274.
Using the same method in reverse (calculating Stoke’s Attack Strength using home goals, and Chelsea’s Defence Strength with away conceded), we calculate that Stoke are likely to score 1.058 goals.
Of course, no games end 1.274 vs. 1.058 – this is simply the average – the result if the match was replayed over and over again.
Poisson Distribution, a formula created by French mathematician Simeon Denis Poisson in the early nineteenth century, allows us to distribute 100% of probability across a range of goal outcomes for each side.
The results are shown in the table below:
The formula itself looks like this: P(x; μ) = (e-μ) (μx) / x!, however, we can use online tools such as this Poisson Distribution Calculator to do most of the equation for us.
All we need to do is enter the different goals outcomes (0-5) in the Random Variable (x) category, and the likelihood of a team scoring (for instance, Chelsea at 1.274) in the average rate of success, and the calculator will output the probability of that score.
This example shows that there is a .280 chance that Chelsea won't score at all, but are almost equally as likely (0.227) to get two goals. Stoke, on the other hand, are mostly likely to score once (0.367), but are far more likely to not score at all then put two past last season’s runners-up. Hoping for a five-nil drubbing? The probability is 0.25% if Chelsea are the scorers, or 0.01% for Stoke to do it.
As both scores are independent (mathematically-speaking), you can see that both teams are most likely to score one goal. If you multiply the two probabilities together, you’ll get the probability of that outcome – 0.131.
There’s a 13.1% chance the match will end 1-1 – or in decimal odds, 7.63.
You can then compare your result to a bookmaker’s odds to help see how they differentiate. For instance, taking into account all possible draw combinations (0-0, 1-1, 2-2, 3-3, 4-4 and 5-5), this method gives odds of 3.585 (a 27.9% probability) that the two sides will draw.
Pinnacle Sports’ odds are 3.870 (a 25.9% probability) – a two percent difference that reflects Pinnacle Sports’ slim betting margins, and will allow you to win more.
This is a simple predictive model that doesn’t allow for correlations, such as the widely recognised pitch effect that shows that matches have some tendency to be either high or low scoring. The system is of greatest benefit over a long period of time – using it for a whole season’s worth of games, rather than one-off matches.
It also ignores situational factors – club circumstances, game status etc. - and subjective evaluation of the change of each team during the transfer window. In this case, it means the huge x-factor of André Villas-Boas’ first Premier League game in charge of Chelsea is entirely ignored.
These are particularly important areas in minor league games, which can gives punters an edge against bookmakers that is hard to achieve in major leagues, given the expertise that modern bookmakers like Pinnacle Sports possess.
If you want to beat the bookmakers at their own game, it is crucially important to get the best odds available, which will usually be found at Pinnacle Sports.